Variable stars

Among the various types of stars, there are some that differ in that they have a cyclic variation in brightness. This variation parallels a corresponding variation in size, rather like a balloon that is periodically inflated and deflated. The time it takes for such a pulsating star to go through one cycle of variation and return to its original brightness is called its period. A period ranges from seconds for some stars to years for others. A few pulsating stars can be seen with the naked eye, although the modern detection technique is to photograph a star field and then compare the result electronically with a photograph of the same field taken at a different time. By this method, any stars that have changed in brightness can be recognized, and hundreds of pulsating stars have now been catalogued. Their strange structural properties provide clues to the history of stellar evolution, and their behavior provides information about the scale of the universe.

Eta Carinae, one of the brightest and most massive stars in the Milky Way, lies at the center of the Eta Carinae Nebula in the southern part of the galaxy. In the early 1600’s, the star was easily visible—its magnitude varied irregularly between 2 and 4. At the beginning of the nineteenth century it began to brighten increasingly. By 1843, it reached a magnitude of —1 and was the second brightest star in the sky (Sirius being the brightest). It then faded and now varies irregularly around the 7th magnitude. Eta Carinae is estimated to be about 100 solar masses and is, therefore, not very stable. Periodically, it casts off a shell of gas, which is seen as an attempt to restore its stability. This puts it into the class of explosive, or catastrophic, variables in which the variation in brightness is caused by an explosive ejection of outer layers.

Cepheid variables

The most studied group of pulsating stars are the Cepheid’s, named after the prototype star Delta Cephei. All have regular periods, which last from 1 to 50 days. They are a relatively rare local sight because there are only about 700 known Cepheid’s in our own galaxy. Delta Cephei is a good example of its type, varying between an apparent magnitude of 3.6 and 4.3, with a period of 5.4 days. Another Cepheid in our galaxy is the North Star, Polaris, whose period is about four days. Although Polaris continues to pulse, its variation in brightness has declined steadily during the 1900’s. The absorption lines in the spectrum of a Cepheid star show Doppler shifts. This indicates that its size may change by 5 or 10 per cent through the course of one pulsation. Surface temperature varies, and the star is brightest during its hottest phase.
It is the observable pulsations in Cepheid’s that give astronomers a means of measuring distances to stars in other galaxies. These pulsations also provide information about the structures and distances within our own galaxy. The period of a Cepheid star, which is measurable in days, is directly related to the average intrinsic brightness of the star. Using this correlation, the value of the intrinsic brightness can be deduced. By comparing this value with the average brightness of the star, as seen from earth, the actual distance of the star from earth can be calculated. The technique is analogous to judging the distance of a car at night from the brightness of its headlights.
Cepheid stars fall into two distinct groups: classical Cepheids, called Type I Cepheids, which are massive young stars that generally appear in open clusters; and W Virginis stars, or Type II Cepheids. This second group comprises older, low-mass stars, most of which occur in globular clusters. But the most important difference between the two groups is that they do not follow the same period-luminosity relationship. Type II Cepheids are 1.5 magnitudes fainter than Type I. The calculated distance measurement depends, therefore, on the type of Cepheid observed. This distinction between the two classes of Cepheid stars was made during the mid-twentieth century, after which all distance measurements had to be revised. This is because Type I Cepheids are intrinsically brighter than had originally been thought. The new findings also meant that the galaxies containing Type I Cepheids are farther away than was originally assumed. The difference in magnitude of 1.5 corresponded to a doubling of the distance to these galaxies. Popular writers of the time, however, reported that the universe had doubled in size!

Light curves of Delta Cepheid and RR Lyrae stars show the relationship between period and luminosity in variable stars. The principle, worked out by Henrietta Leavitt in 1912, states that the longer a star’s period is, the brighter it becomes. The average period of Delta Cepheid is 5.4 days, and it reaches an apparent magnitude of 3.6. (Luminosity increases as magnitude becomes smaller.) RR Lyrae stars have periods that last only hours, and they reach an average apparent magnitude of 7.1; they are, thus, less bright than Cepheid’s.

RR Lyrae variables

RR Lyrae variable stars pulsate in the same way as Cepheids, but they have shorter periods, lasting from one day to only a few hours. These stars are also referred to as duster variables because they are found in globular clusters. All RR Lyrae stars are in the same stage of evolution, having a similar mass, age, and chemical composition. In addition, they all have a similar intrinsic brightness (of approximately 0 on the magnitude scale), making distance measurements even easier to calculate for RR Lyrae variables than for Cepheids. Once the exact intrinsic brightness of a star has been determined, a comparison with the apparent brightness gives its distance. The distance of the cluster in which it appears can then be deduced, as well as the luminosity and sizes of all the cluster stars.

Eclipsing binary stars orbit around their common center of mass and alternately block each other’s light. The yellow star in this example emits more light than its bigger red companion. When the small star passes in front of the larger one (1), the total amount of light emitted decreases slightly. But when the smaller, brighter star moves behind the larger one (2), the total apparent magnitude is greatly reduced. Eclipsing binaries of the same size may completely occlude each other.

Long-period variables

Giant red and supergiant stars are the most numerous types of variable stars. Their periods are not as consistently regular as those of Cepheids and RR Lyrae stars. Most of their periods are from three months to two years. The brightest example of this type is Mira, a giant red star in the constellation of Cetus. At its faintest, it is invisible to the naked eye, having an apparent brightness of 9, but it becomes brighter over a period of 11 months and at maximum brightness, is a quite prominent object in the night sky.

Eclipsing binaries

Many stars are part of a double-star system, each member traveling in its own orbit around their common center of mass. Occasionally, the orbits of the double stars are so aligned that, seen from the earth, each star masks the other as the two move around each other. The light from the pair (called an eclipsing binary) varies, not because of a variation in the intrinsic luminosity of the stars, but simply because one star periodically blocks out the light from the other. The most prominent eclipsing binary star in the local system is Algol, in the constellation of Perseus.